Some Examples and Counterexamples about Continuity on Equilibrium Problems

This paper attempts to underline how the Diagonal Transfer Continuity hypothesis (Baye, Tian and Zhou, 1993) and Better-Reply Security (Reny, 1999) are unconnected between themselves as sucient conditions for stating the existence of Nash equilibria. Besides, various examples and counterexamples regarding Nash equilibria existence Theorem (Baye, Tian and Zhou, 1993) and extensions of maximum existence results for bifunctions established for a function of one variable (Baye and and Zhou,1995). We present, also, a sucient conditions for Diagonal Transfer Continuity. Moreover, an example of quasi-concave game having multiple Nash equilibria, in which the aforesaid hypotheses and other improvements (Lignola, 1997) fall, is presented.